Moreover, $gcd(3, \phi(N)) = 3$, meaning that we can’t invert the decryption! We have to compute all possible cube roots of the ciphertext. All such algorithms work modulo prime, but that is not a problem, since we have the factorization: we will compute all cube roots modulo each prime and then use Chinese Remainder Theorem to reconstruct the answer modulo $N$. There are some algorithms described in the following paper: New Cube Root Algorithm Based on Third Order Linear Recurrence Relation in Finite Field. The shortest one is the Cipolla-Lehmer algorithm, so I decided to implement it. Here’s Sage function:

Note that it yields some cube root. We need to get all of them (at most 3) modulo each prime. We can either extract random cube roots with cube_root until we get all of them, or we can simply multiply a single root by 3rd roots of unity. We can get these roots by finding a multiplicative generator and raising it to power $(p-1)/3$.